1. Introduction

2. Technical choices
   (R and relating packages)

3. {Cartograflow} general overview

4. Case study

5. Conclusion
   (To do and remaining challenges)

• General aim: geovisualisation of spatial interactions patterns through flows on thematics maps, clearly (as Tobler's said)

• The first problem to solve is to reduce the graphic complexity ("spaghetti-effect") due to the representation of N(N-1) links and (N) places
  

• How to plot on a map - in am meaningfull way - origin-destination linear features ?

This comes after: Bahoken (2016), Contribution à la cartographie d'une matrice de flux appendices
https://halshs.archives-ouvertes.fr/tel-01273776

1. Graphic, retinan ;
   
2. Geo-cartographic information (background) ;
   
3. Statistical or numeric information:
   – on places of origine (i) and/or destination (j)) - punctual features ;
   – on interactions (Fij) between (i) and (j) - mostly linear features,

In order to reduce the flow data values or features by:
- clusterisation / aggregation ;
- selection / thresholding

The choice of R/Rstudio rather than GIS software or purely statistical tools:

• (relatively) easy to handle ;
  
• open access and (easily) accessible ;
  
• provide reproducible research in the specific cartographic area ;
  
• facility of writing documents (with .Rmd formats) for educational purposes
  (here it is ioslides_presentation rendering in html from .Rmd)

MATRIX FILTERING

{igraph} and {matrix}
- general packages for mathematical playing with matrixes ;

{flows} Laurent Beauguitte et al. (2016)
- dedicated to local flow selection as a variant of Nyusten & Dacey (1961) dominant flow

{migR} Matthieu Garnier et al. (2019)
- focused on residential migrations indicators computation and local flow mapping

{stplanR} Robin Lovelace (2016)
- dedicated to some transportations issues, for planar graphs

MATRIX MAPPING

{igraph} and {ggplot2} Hadley Wickham (en 2005)
- general packages for plotting and no geographic links features

{cartography} Timotée Giraut & Nicolas Lambert (2015)
- dedicated to thematic, mainly choropleth cartography with various way of representation and advanced thematic mapping rendering options
- limited for flow mapping to small and symmetric matrixes

• Dedicated to general OD issues, i.e. for non planar networks that required global thresholding (to this day) ;
  

• Allows spatial filtering procedure, via an external matrix of (XY) positions:
  Compute continuous or discrete distance travelled by the flow :
  

• Filtering procedures with embedded flow mapping process:
  – provide integrated plotting function ;
  – allow to plot graduated and (non) oriented straight lines

• List format "L":
  a .csv 3 column flow dataset (origin, destination, flow_value)

• Matrice format "M":
  a .csv [n*n] flow dataset.

flowtabmat():
- to convert from "L" to "M" format - as {base::dcast} ;
- to check if your matrix is square or not ;

flowcarre():
- to close and square [n,n] an asymetric matrix ;
- from "L" or "M" format.

flowtype():
- to compute the main types of flows from descriptive analysis
(from an asymmetric flow matrix, in "M" or "L" format) ;
- result is (as Tobler's) bilateral gross or net flows (symetric and skew symetric) matrix.

flowjointure():
- to perform an attribute spatial join - by (i) and (j) between a .csv flow dataset and a .shp spatial shape ;
- to transfert the OD centroïd coordinates (Xi, Yi, Xj, Yj) of a .shp areal background to the flow matrice.

flowreduct():
- for filtering flows by an external matrix (e.g. a matrix of continuous distance).
- the select criterion set as:
– dmin is for selecting the min value to plot - ie. up to x km ;
– dmax is for selecting values - ie. less than x km

flowgini():
- performs a concentration analysis of a flow dataset ;
- computes Gini coefficient and plot interactive Lorenz curve
- to be use before flowanalysis()

flowanalysis():
- to compute a global filter criterion based on
– flow's significativity (% of total interactions) ;
– and/or flow's density (% of total linear features).

flowdistance():
- for computing a continuous distance with several additional parameters ;
- for filtering flows by a distance travelled

flowcontig();
- compute a discrete (ordinal) distance matrix based on (k) contiguïty ;
- where (k) is the rank parameter (1:n-1) defined as the number of borders to be crossed between origins and destinations places

flowmap():
- is for plotting OD flows ;
- by filtering values or features, or not ;
- with straight features, oriented (arrows) or not

• Statistical dataset :
  "Base flux de mobilite" MOBPRO - commuters - INSEE, 2015

• Geographical dataset :
  municipalities from IGN, data preparation by APUR & UMS Riate, 2017

## 'data.frame':    4692 obs. of  3 variables:
##  $ i  : int  75101 75101 75101 75101 75101 75101 75101 75101 75101 75101 ...
##  $ j  : int  75102 75105 75108 75109 75112 75113 75115 75116 92012 92026 ...
##  $ Fij: int  247 104 426 263 123 139 134 123 128 139 ...

## Reading layer `MGP_communes' from data source `D:\R\ECTQG\fdc_data\MGP_communes.shp' using driver `ESRI Shapefile'
## Simple feature collection with 150 features and 10 fields
## geometry type:  POLYGON
## dimension:      XY
## bbox:           xmin: 637297 ymin: 6838631 xmax: 671756 ymax: 6879246
## epsg (SRID):    NA
## proj4string:    +proj=lcc +lat_1=49 +lat_2=44 +lat_0=46.5 +lon_0=3 +x_0=700000 +y_0=6600000 +ellps=GRS80 +units=m +no_defs

Plotting these matrix on a map reveals the so-called spaghetti-effect
Hereby, plotting of all theoretical OD links (without filter)

Global criteria means unique parameter to be apply to all the cells of the matrix

#eg : the mean value
tabflow <-tabflow %>% 
  filter(tabflow$Fij!=0)  # matrix reduction to existing flow values

X<-mean(tabflow$Fij)      

flowmap(tab = tabflow,
                 format="L",
                 fdc="./fdc_data/MGP_communes.shp",
                 code="IDCOM",
                 filter=TRUE,
                 a.col="#3f4247",
                 threshold= X   #flow value > X = 348
                )

Plotting flow value up to the criteria Fij > alpha
alpha=348 (mean value)

(1/3) Computes Gini's coefficent

tab_gini<-flowgini(tabflow.sq, format="L", origin="i",dest="j", valflow="ydata",
          fdc = "./fdc_data/MGP_communes.shp",code="IDCOM", lorenz.plot = FALSE)

head(tab_gini)

##          i     j ydata       X1      Y1       X2      Y2 link     flowcum
## 1067 75117 75108  4857 649165.4 6865479 649575.7 6863852    1 0.003117114
## 1065 75115 75108  4852 648097.2 6860237 649575.7 6863852    1 0.006231019
## 1066 75116 75108  4000 645848.7 6862519 649575.7 6863852    1 0.008798130
## 1068 75118 75108  3560 652206.2 6866034 649575.7 6863852    1 0.011082859
## 2281 92012 75116  3263 644144.9 6859859 645848.7 6862519    1 0.013176979
## 4515 75115 92012  3142 648097.2 6860237 644144.9 6859859    1 0.015193445
##           linkcum
## 1067 0.0002292001
## 1065 0.0004584002
## 1066 0.0006876003
## 1068 0.0009168004
## 2281 0.0011460005
## 4515 0.0013752006

(2/3) Plot Lorenz curve

(3/3) Compute critflow parameter and flowmap

flowanalysis(tab_gini, critflow = 0.02, result = "signif")

## [1] "threshold =  3070  ---  flows =  2 % ---  links =  0.18 %"

(3-bis) Compute critlink parameter and flowmap

flowanalysis(tab_gini,critlink = 0.01,result = "density")

## [1] "threshold =  2045  ---  flows =  7.21 % ---  links =  1 %"

Plot 4 % of the total features, flow greater than 2015

• Spatial means filtering by the distance travelled between origin and destination ;
  
• Involves a matrix distance - so the criteria is continuous

4 steps involved:
- 1) compute a distance matrix ;
- 2) plot the corresponding graph ;
- 3) filter the matrix ;
- 4) Reduce the flow matrix by the filtered distance matrix

(1/3) Compute continuous distance matrix from a shapefile (through jointure)
Can be done with a .csv in {base}

tab.distance<-flowdist(tab, dist.method = "euclidian",result = "dist")
head(tab.distance)

##       i     j  distance
## 1 75101 75102  787.3099
## 2 75101 75105 2270.1051
## 3 75101 75108 2087.3999
## 4 75101 75109 1629.7126
## 5 75101 75112 6948.2107
## 6 75101 75113 4240.7855

(2/3) Reduce the distance matrix
Example: Compute the summary to choose the threshold criterion. The short distance (as Dij< Q1)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##       0    3793    7016    7586   10619   27067

Reduce the flow dataset from a selected distance travelled Dij < 3793 m (Q1)

tab.flow.dmin<-flowreduct(tabflow.sq,tab.distance,metric = "continous",
                     select = "dmax", # max distance parameter to plot 
                     d = 3793)        # corresponding max distance value to plot
#select for all i,j flow values up to 0
flow.dmin<-tab.flow.dmin%>%
        select(i,j,flowfilter)%>%
        filter(flowfilter !=0)

(3/3) Reduce the flow matrix by the distance matrix filtered

(1/2) Building the neighbouring graph (ex. rank 1)

Reduce the flow matrix to only selected neighbouring flow values

• This is a 1st version of {cartograflow} dedicated to global filtering ;
  
• It combines the application of a filtering criterion with a plotting procedure ;
  
• Two matrix format are available, for direct compatibility with statistical and thematic mapping packages ;
  
• A voluntary simple, general and generalizable approach for pedagogic issues
  

• DATA FORMAT
  
  – Loading an (X,Y) .csv file in flow mapping procedure ;
  – Trying to playing with complex data sets (i.e. temporal, categorial)
  

• DRAWING FEATURES
  
  – Dissociation and rendering of arrows in parallel ;
  – Rendering arrows as a curve ;
  – Trying edge bundling procedures ;
  

• DATA FILTERING
  
  – Adding local filtering:
  selecting nodes ;
  applying dominant flows analysis for drawing selected links ;
  – Adding complementary contiguity matrix, ex. Queen neighbours ;
  – Adding matrix reduction by clustering, especially after dominant analysis

THANKS FOR YOUR ATTENTION

Cartograflow
– CRAN: https://cran.r-project.org/web/packages/cartograflow/index.html
– Github: https://github.com/fbahoken/cartogRaflow

All collaborations are welcome !

Françoise BAHOKEN
IFSTTAR / AME-SPLOTT
Ass. UMR 8504 Géographie-Cités
francoise.bahoken@isffar.fr
@fbahoken